When a geometric modeling of a hull form for ship design and hull production is done, a hull fairing is a tedious process which wastes a lot of time, but it is unavoidable because hull consist of the sculptured surfaces. This paper presents the mathematical method of the direct fairing to overcome the tediousness of cross fairing. Bi-cubic B-spline surface description was adopted for the representation of the hull surface. The fairing process was executed by minimizing the strain energy in a shell plate. The color-encoded Gaussian curvature and strain energy were visualized on the screen to illustrate the fairness of the surface. The geometric information generated from the faired hull surface model was interfaced with the basic design calculation package and the hull production system.

Three-dimensional nonlinear sloshing effects due to tank motions are simulated by solving boundary value problem using the panel method based on boundary integral technique. While Shinkai used boundary elements on which source strengths vary linearly between nodes, the source of constant strength is distributed on each triangular panel in the present study. The source strength at each time step is determined by solving the Fredholm integral equation of the second kind obtained from Green's theorem. To avoid cumulative numerical errors as time elapses, Adam-Bashforth-Moulton method is employed. Numerical examples for the case of partially filled spherical tank on board oscillating in harmonic sway mode or pitch mode are solved. The elevation of the free surface is compared with the result by Shinkai and confirmed in good agreement during early time. The input and the output energy are comparatively evaluated to check the overall accuracy of the present numerical scheme. Although some leakage of energy are found as time marches, it is plausible when we take into account nonlinearities of the problem and the number of panels of the model.

The complete, fully-elliptic Reynolds-averaged Navier-Stokes equations have been solved using a two-layer model, in the turbulence model, for the axisymmetric body. Numerically generated boundary-fitted coordinate system and the finite analytic methods are used to solve the governing equations. Calculations are started after the middle body with given inlet conditions. The velocities and the turbulent quantities at the inlet section are specified by solving the boundary layer equations or by standard flat-plate boundary profiles. The effects of the inlet conditions on the solution are investigated.

In this paper the nonlinear free surface flows for an axisymmetric submerged body oscillating beneath the free surface are solved and the forces acting on the body are calculated. A boundary integral method is applied to solve the axisymmetric boundary value problem and the Runge-Kutta 4-th order method is used for the time stepping of the free surface location. The nonlinear forces acting on the axisymmetric body are computed and compared with published results.

In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of and are assumed to be bilinear on the subdivided surface. The singular part proportional to are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

By employing multiple-scale expansion techniques, the diffraction of sinusoidally-modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is found that the evolution of diffracted waves can be described by the Zakharov equation to the leading order and it can be replaced by the cubic equation with an additional linear term for stable modulations. Computations are made for the cubic equation with different values of nonlinear and dispersion parameters. Numerical results well reflect the experimental findings in the amplitude and width of generated stem waves. It is numerically confirmed that the nonlinearity dominates the wave field, while the dispersion hardly affects the wave evolution, and stem waves are likely to be formed for steep incident waves in the case of stable sinusoidal modulations.

The updated Lagrangian Finite Element Method is introduced to analyse rigid body-fluid impact problem which is characterized by incompressible Navier-Stokes equations and impact-contact conditions between free surface and rigid body. For the convenience of numerical computation, velocity fields are splinted into vicous and pressure parts, and then the governing equations and boundary conditions are decomposed in accordance with the decomposition. However, Viscous stresses acting an the solid boundaries are neglected on the assumption that very small velocity gradients may occur during extremely small time interval of the impact. Four coded quadrilateral elements are used to discretize the space domain and the fully explicit time-marching algorithm is employed with a reasonably small time step. At the beginning of each time step, contact velocity of the rigid body is computed from the momentum balance between the body and the fluid. The velocity field is then computed to satisfy the discretized equations of motions and incompressibility and contact constraints as well as an exact free surface boundary condition. At the end of each time step, the fluid domain is updated from the velocity field. In the present time stepping numerical analysis, behaviour of the free surface near the body can be observed without any difficulty which is very important in the water impact problem. The applicability of the algorithm is illustrated by a wedge type falling body problem. The numerical solutions for time-varying pressure distributions and impact loadings acting ion the surface are obtained.

The dynamic stability of the long vertical beam subjected to the periodic axial load is investigated. As a solution method, the Galerkin's method is used to obtain a set of coupled Mathieu type equations. To obtain the stability chart, both the perturbation method and numerical method are used, and the results of the both methods are compared with each other. The stability regions for the various boundary conditions are obtained, Also the effects of the viscous damping, the mean tension and the multi-frequency parametric excitation are studied in detail.

In this paper the dynamic analysis of the multi-span beam on elastic foundation, which include discrete transnational and rotational springs, was performed. Furthermore, the effects of the intermediate supports were investigated. As a solution method, first the orthogonal polynomial functions which satisfy both the geometric and dynamic boundary conditions are obtained by imposing the orthogonality conditions. Then, the Galerkin's method is used to obtain the natural frequencies of the system. From numerical tests for various constraint and boundary conditions, it was found that the higher order orthogonal polynomial functions obtained by the present method can be used to get the accurate solution.

The structures such as railway bridges can be modelled as the multi-span beam on the elastic foundation. These structures are usually subject to the moving load, which has a great effect on dynamic stresses and can cause severe motions, especially at high velocities. In this paper, the dynamic responses of the multi-span beam on the elastic foundation were obtained by using the Galerkin's method and the numerical time integration technique. As trial functions, the same orthogonal polynomial functions obtained in part 1, were used. From the numerical results, it was found that the one term expansion of the assumed solution usually leads to the accurate solutions. However, in the case that the stiffness of the transnational spring is very high or the rotational spring is placed where the slope of the first mode is zero, the higher modes must be included to obtain the accurate solutions.

In the course of ship basic design, the redesign works to avoid resonance can be carried out efficiently provided that the frequency sensitivities of the baseline system is available. In this paper, for lower modes of ship's hull vibrations, a practical method to predict the natural frequency sensitivities to major design variables subject to considerations at the preliminary design stage is presented. The method is of derivation based on frequency sensitivities of uniform Timoshenko beams eguivalent to actual ships.

In the non-linear behavior of many materials, there is difference between the monotonic behavior by static load and the cyclic behavior by cyclic load. In particular, the short fatigue cracks to propagate in elasto-plastic stress concentrations(notches), are governed significantly by the cyclic behavior of materials. Accordingly, it is needed to investigate and compare the monotonic and cyclic behavior of materials. In the pressent study, the stress-strain relations of materials by monotonic and cyclic load tests were examined for 2 kinds of steels(SS41, HT80) and 5 kinds of Al-alloys(A5083-O, A6N01-T5, A7N01-T4, A7016-T6, A7178-T6). And the constants for mechanical properties of the materials were determined by experimental results, Moreover, when a notch was subjected to cyclic load, the effect of cyclic hardening property of materials on the variation of stress-strain amplitude in the notch tip was discussed by the application of Neuber's rule and experiments for a center notched plate.

In this paper, a method to overcome inefficiency of the finite element method in the calculation of compressive strength of one-sided stiffened plates, is proposed. In this method the collapse modes of stiffened plates are assumed as follows. a) Overall buckling Overall collapse b) Local buckling Overall collapse c) Local buckling Local collapse In each collapse mode, shape of deflection is assumed, and then elastic large deformation analysis based on the Rayleigh-Ritz method is carried out. One-sided stiffening effect is considered by taking into account of the moment due to eccentricity. Plastic analysis by assuming hinge lines is also carried out. The ultimate strength of a stiffened plate is obtained as the point of intersection of the elastic analysis curve and the plastic one. From this study, it is concluded that the angles between the plastic hinge lines in plastic collapse mode are determined as the ones which give the minimum collapse load, and these angles are different from the ones assumed in the previous studies. Minimum stiffness ratios can also be calculated. Calculated results according to this method show good agreements with the results by the finite element method.

In this paper, an efficient method for the analysis of damage and strength of double bottom structure in stranding is described by using idealized structural unit method. Also a procedure for the determination of the effective double bottom height which is required in order to protect the inner-bottom plate is proposed. In the comparison between the present solution and he existing experimental and numerical results in stranding, its observed that the present method gives reasonable results requiring very shorts computiong times. The present method is then applied to the double bottom structure of 40K product oil carrier which is designed by the double skin design concept as an example. By performing the series of analysis, the influence of vertical member space, plate thickness and double bottom height on the energy absorption capacity of the double bottom structure in stranding is investigated. Also the minimum double bottom height with varying each design variable Is calculated based on the above result.

In this paper, an efficient method for the ultimate longitudinal strength analysis of the double skin hull girder is presented by using idealized structural unit method. Idealized plate element subjected to biaxial load is developed taking account of initial deflection and welding residual stress. Interaction effect between local and global buckling in the whole structure is also taken into consideration. The reserve strength factor and reliability index for the example 40K double skin product oil carrier are evacuated against the ultimate longitudinal strength. It is concluded that the prudent method seems to be useful in the sense that the computing time required is very short while giving the reasonable solution.

A practical procedure for the ultimate compressive strength-based safety and reliability assessment of the double skin upper deck structure is described. The external compressive stress acting on the upper deck structure which is due to the still water and wave-induced sagging moment is approximately estimated by using the existing rule of classification society. The ultimate compressive stress of double skin structure under the action of sagging moment is analyzed by using idealized structural unit method. Here an idealized plate element subjected to uniaxial load is formulated by idealizing the nonlinear behaviour of the actual element taking account of the initial imperfections in the form of initial deflection and welding residual stress. The interaction effect between the local and global failure in the structure is also taken into consideration. The accuracy of the present method is verified comparing with the present solution and the existing numerical and experimental results for unit member and welded box columns. The safety of the structure is evaluated using the concept of conventional central safety factor and the reliability assessment is made by using Cornel's MVFOSM method. The present procedure is then applied to upper deck structure of double skin product oil carrier. The influence of the initial imperfections and the yield stress of the material on the safety and reliability of the structure is investigated.

In this study, an analytical solution of pre-buckling, buckling, post-buckling, ultimate strength and post-ultimate strength behaviour of simply supported rectangular plates subjected to biaxial compression is derived. Parametric study with varying the aspect ratio, the slenderness ratio and the loading ratio is carried out. The present solution may be used as basical data when the verfication of the numerical and experimental result is made.

The modified arc-length algorithms for the automatic incremental solution of nonlinear finite element equations proposed by Riks are presented, which comprise the cylindrical arc-length method and the normal arc-length method. These methods are developed to trace the nonlinear path of large displacement problems such as a pre and post bucking/collapse response of general structures. These methods are applied to analyse the nonlinear behavior of arch and shell problems in parallel with the standard and modified Newton-Raphson method.

This paper is an illustration of the application of the reliability analysis to the transverse structure of a SWATH ship. The ultimate strength of plate members on the cross structure and upper part of strut are considered in the reliability analysis. The fatigue reliability analysis has been also carried out at the junction of cross structure, sponsors and strut. Included is also an example of the allowable fatigue damage level. Demonstrated is the reliability study of series system of which elements are the ultimate and fatigue failure as well. Doing this would be desirable to get a truer solution of the structural safety level. The paper ends with a brief summary of the present reliability study and same important points which may be useful at the design stage.

A methodology of constructions a mathematical cost model for an activity constituting ship hull assembly process is proposed. The relationship between number of workers and processing time required for an activity can be formulated using an work study method, then manhours and shop floor area-hours required are calculated accordingly. The costs for unit manhour and unit shop floor area-hour respectively are calculated by distributing the overall annual cost of the company to the overall production resources consummed during the year. A general procedure of implementing the methodology has been demonstrated through a test on an exampled activity drawn from a real process.